Abstract: A safety brake for hydraulic rams, particularly for hydraulic elevators, includes a plurality of braking members disposed around the piston in a circular array. The outer surfaces of the spaced apart braking members together form the shape of a truncated cone, and the inner surface of a stationary housing surrounding the brake members is complementarily shaped. The angle of inclination of the two conical surfaces is small, and the braking members move downwardly and inwardly only a short distance to engage the piston, so that the conical geometry of the brakes and housing surfaces does not produce significantly mismatched sliding surfaces as the brake members move downwardly.